TWITTER EVENT NETWORKS AND THE SUPERSTAR MODEL

• 成果类型: Article
• 署名作者: Bhamidi, Shankar; Steele, J. Michael; Zaman, Tauhid
• 署名单位: University of North Carolina; University of North Carolina Chapel Hill; University of Pennsylvania; Massachusetts Institute of Technology (MIT)
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/14-AAP1053
• 发表日期: 2015
• 页码: 2462-2502
• 关键词: branching-processes; GROWTH; graphs; trees

摘要

Condensation phenomenon is often observed in social networks such as Twitter where one superstar vertex gains a positive fraction of the edges, while the remaining empirical degree distribution still exhibits a power law tail. We formulate a mathematically tractable model for this phenomenon that provides abetter fit to empirical data than the standard preferential attachment model across an array of networks observed in Twitter. Using embeddings in an equivalent continuous time version of the process, and adapting techniques from the stable age-distribution theory of branching processes, we prove limit results for the proportion of edges that condense around the superstar, the degree distribution of the remaining vertices, maximal nonsuperstar degree asymptotics and height of these random trees in the large network limit.